Altitude and metabolic syndrome in China: Beneficial effects of healthy diet and physical activity

Background The correlation between altitude and metabolic syndrome has not been extensively studied, and the mediation effects of diet and physical activity remain unclear. We evaluated the cross-sectional correlations between altitude and metabolic syndrome and the possible mediation effects of diet and physical activity in China. Methods We included 89 485 participants from the China Multi-Ethnic Cohort. We extracted their altitude information from their residential addresses and determined if they had metabolic syndrome by the presence of three or more of the following components: abdominal obesity, reduced high-density lipoprotein cholesterol (HDL-C), elevated triglycerides, elevated glucose, and high blood pressure at recruitment. We conducted multivariable logistic regression and mediation analyses for all and separately for Han ethnic participants. Results The participants had a mean age of 51.67 years and 60.56% were female. The risk difference of metabolic syndrome was -3.54% (95% confidence interval (CI) = -4.24, -2.86) between middle and low altitudes, -1.53% (95%CI = -2.53, -0.46) between high and low altitudes, and 2.01% (95% CI = 0.92, 3.09) between high and middle altitudes. Of the total estimated effect between middle and low altitude, the effect mediated by increased physical activity was -0.94% (95% CI = -1.04, -0.86). Compared to low altitude, the effects mediated by a healthier diet were -0.40% (95% CI = -0.47, -0.32) for middle altitude and -0.72% (95% CI = -0.87, -0.58) for high altitude. Estimates were similar in the Han ethnic group. Conclusions Living at middle and high altitudes was significantly associated with lower risk of metabolic syndrome compared to low altitude, with middle altitude having the lowest risk. We found mediation effects of diet and physical activity.

Mediation analyses of altitude (binary) and mediators physical activity and dietary pattern (continuous) on metabolic syndrome Figure S1A Adjusted risk difference for metabolic syndrome comparing middle altitude group to low altitude group Figure S1B Adjusted risk difference for metabolic syndrome comparing high altitude group to low altitude group Figure S1C Adjusted risk difference for metabolic syndrome comparing high altitude group to middle altitude group

The definition of proportion mediated in the causal mediation analysis
The approach to Causal mediation analysis was proposed by Imai, et.al. [1,2] R package mediation consists of a comprehensive suite of statistical tools has been developed to implement causal mediation analysis. [3] The general framework for the mediation analysis is represented as follow (the text in grey may be skipped for the first read): Suppose ( ) denote the potential outcome of unit under the treatment status (where = 0, 1), and ( ) denote the potential value of the mediator for unit under the treatment status t. The causal mediation effects or indirect effects for each unit are as follow: Similarly, the direct effects of the treatment for each unit are defined as follows: Then, the total effect of the treatment is decomposed into the causal mediation effects and direct effects: If we add the assumption that there is no interaction between causal mediation effects and direct effects (i.e., = (1) = (0) and = (1) = (0)), then the total effect can be simplified as: Where is the mediated (indirect) effect and is the direct effect. The proportion mediated, the magnitude of the average causal mediation effects relative to the average total effect, can be defined as: which is the ratio of the average causal mediation effects to the average total effect. This proportion-mediated measure can be a helpful summary, as in some sense it captures how important the pathway through the intermediate is in explaining the actual operation of the effect of the exposure on the outcome.

The dilemma of confidence interval of proportion mediated in the causal mediation analysis
The proportion mediated makes sense when the sign of the average causal mediation effects is the same as the sign of the direct effects. It is problematic when the sign of the causal mediation effects and direct effects operate in different directions, which can result in a proportion mediated larger than 100% and such measure may be not meaningful (2 nd paragraph, Page 48 [4] ).
The R package mediation conducts a Monte Carlo experiment to investigate the finite-sample performance of the average causal mediation effect, direct effect and the proportion mediated. Briefly, take a random sample with replacement of size n from the original data J times. For each of the J bootstrapped samples, proportion mediated was computed as mediation effects/(direct effects + mediation effects) (as the equation (5)) for each sample, and then using percentiles for the confidence interval (CI) limits.
Among the J bootstrapped samples, if direct effects and mediation effects have opposite signs in a sample, the proportion mediated from this sample is greater than 1(or less than -1). Then the percentile among the J bootstrapped samples, which is the confidence interval of proportion mediated, could be outside [0,1]. Similar awkwardness arises in the help document of the "mediation" package; see page 7 of https://cran.r-project.org/web/packages/mediation/vignettes/mediation.pdf.
In our study, the point estimate of proportion mediated was legitimate, as our point estimates of direct and indirect effects were both negative. However, the 95% CI of proportion mediated exceeded 1. In 88% the bootstrapped samples, the direct and mediation effects were both negative, and proportion mediated was reasonably calculated. But in the rest 12% bootstrapped samples, the mediation effects were negative and the direct effects were positive, so the proportion mediated from these sample is larger than 1, resulting in an overall 95% CI with upper limit being